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What does the volume-averaged water age distribution function reveal about flow fields in rectangular shallow reservoirs?

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Abstract

Shallow reservoirs are hydraulic structures widely used for water storage or as sedimentation tanks. Their design and sizing are intricate due to the complex flow fields developing in such structures, hence suitable indicators are needed to evaluate their hydraulic performance. Based on the outcomes of a depth-averaged computational model, we analysed the potential of the distribution function of the volume-averaged water age to unveil in a concise way valuable information on the flow field in rectangular shallow reservoirs. Ten different reservoir layouts were examined. In all cases, the shape of the computed distribution function reveals a remarkable amount of information on the flow field in the reservoirs. The distribution functions exhibit a sequence of steps, followed by an exponential decay, which may be related to fast and slow pathways travelled by water particles along their routes across the reservoirs. As such, the distribution function of the volume-averaged water age was found to provide valuable information for assessing the hydraulic performance of shallow reservoirs, while achieving an effective reduction in the problem dimensionality.

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References

  1. Dufresne M, Vazquez J, Terfous A, Ghenaim A, Poulet J-B (2009) Experimental investigation and CFD modelling of flow, sedimentation, and solids separation in a combined sewer detention tank. Comput Fluids 38:1042–1049

    Article  CAS  Google Scholar 

  2. Isenmann G, Dufresne M, Vazquez J, Mose R (2017) Bed turbulent kinetic energy boundary conditions for trapping efficiency and spatial distribution of sediments in basins. Water Sci Technol 76:2032–2043

    Article  Google Scholar 

  3. Sebastian C, Becouze-Lareure C, Lipeme Kouyi G, Barraud S (2014) Event-based quantification of emerging pollutant removal for an open stormwater retention basin - loads, efficiency and importance of uncertainties. Water Res 72:239–250

    Article  Google Scholar 

  4. Tsavdaris A, Mitchell S, Williams JB (2015) Computational fluid dynamics modelling of different detention pond configurations in the interest of sustainable flow regimes and gravity sedimentation potential. Water Environ J 29:129–139

    Article  CAS  Google Scholar 

  5. Adamsson Å, Stovin V, Bergdahl L (2003) Bed shear stress boundary condition for storage tank sedimentation. J Environ Eng 129:651–658

    Article  CAS  Google Scholar 

  6. Guzman CB, Cohen S, Xavier M, Swingle T, Qiu W, Nepf H (2018) Island topographies to reduce short-circuiting in stormwater detention ponds and treatment wetlands. Ecol Eng 117:182–193

    Article  Google Scholar 

  7. Persson J, Wittgren HB (2003) How hydrological and hydraulic conditions affect performance of ponds. Ecol Eng 21:259–269

    Article  Google Scholar 

  8. Persson J (2000) The hydraulic performance of ponds of various layouts. Urban Water 2:243–250

    Article  Google Scholar 

  9. Persson J, Somes NLG, Wong THF (1999) Hydraulics efficiency of constructed wetlands and ponds. Water Sci Technol 40:291–300

    Article  Google Scholar 

  10. Liu X, Xue H, Hua Z, Yao Q, Hu J (2013) Inverse calculation model for optimal design of rectangular sedimentation tanks. J Environ Eng (US) 139:455–459

    Article  CAS  Google Scholar 

  11. Lakzian E, Saghi H, Kooshki O (2020) Numerical simulation of sediment deposition and trapping efficiency estimation in settling basins, considering secondary flows. Int J Sedim Res 35:347–354

    Article  Google Scholar 

  12. Izdori F, Semiao AJC, Perona P (2019) The role of environmental variables in waste stabilization ponds’ morphodynamics. Front Environ Scince 7:159

    Article  Google Scholar 

  13. Goula AM, Kostoglou M, Karapantsios TD, Zouboulis AI (2008) A CFD methodology for the design of sedimentation tanks in potable water treatment. Case study: the influence of a feed flow control baffle. Chem Eng J 140:110–121

    Article  CAS  Google Scholar 

  14. Zhang J-M, Lee HP, Khoo BC, Peng KQ, Zhong L, Kang C-W, Ba T (2014) Shape effect on mixing and age distributions in service reservoirs. J Am Water Works Assoc 106:E481–E491

    Article  Google Scholar 

  15. Claude N, Secher M, Deng J, Valette E, Duclercq M (2020) Numerical modeling of flow and sediment transport in a real shallow reservoir: Comparison between 2D and 3D simulation. In: River Flow 2020-Proceedings of the 10th Conference on Fluvial Hydraulics, (pp. 331–339)

  16. Dufresne M, Vazquez J, Terfous A, Ghenaim A, Poulet J-B (2009) CFD modeling of solid separation in three combined sewer overflow chambers. J Environ Eng 135:776–787

    Article  CAS  Google Scholar 

  17. Tarpagkou R, Pantokratoras A (2013) CFD methodology for sedimentation tanks: the effect of secondary phase on fluid phase using DPM coupled calculations. Appl Math Model 37:3478–3494

    Article  Google Scholar 

  18. Li H, Sansalone J (2021) CFD with evolutionary optimization for stormwater basin retrofits. J Environ Eng (US) 147:04021017

    Article  CAS  Google Scholar 

  19. Rowland JC, Stacey MT, Dietrich WE (2009) Turbulent characteristics of a shallow wall-bounded plane jet: Experimental implications for river mouth hydrodynamics. J Fluid Mech 627:423–449

    Article  Google Scholar 

  20. Canestrelli A, Nardin W, Edmonds D, Fagherazzi S, Slingerland R (2014) Importance of frictional effects and jet instability on the morphodynamics of river mouth bars and levees. J Geophys Res Oceans 119:509–522

    Article  Google Scholar 

  21. Milovanovic I, Bareš V, Hedström A, Herrmann I, Picek T, Marsalek J, Viklander M (2020) Enhancing stormwater sediment settling at detention pond inlets by a bottom grid structure (BGS). Water Sci Technol 81:274–282

    Article  Google Scholar 

  22. Grayman WM, Rossman LA, Deininger RA, Smith CD, Arnold CN, Smith JF (2004) Mixing and aging of water in distribution system storage facilities. J Am Water Works Assoc 96:70–80

    Article  CAS  Google Scholar 

  23. Stovin VR, Saul AJ (2000) Computational fluid dynamics and the design of sewage storage chambers. Water Environ J 14:103–110

    Article  CAS  Google Scholar 

  24. Dufresne M, Dewals BJ, Erpicum S, Archambeau P, Pirotton M (2010) Classification of flow patterns in rectangular shallow reservoirs. J Hydraul Res 48:197–204

    Article  Google Scholar 

  25. Peltier Y, Erpicum S, Archambeau P, Pirotton M, Dewals B (2014) Experimental investigation of meandering jets in shallow reservoirs. Environ Fluid Mech 14:699–710

    Article  Google Scholar 

  26. Dewals BJ, Kantoush SA, Erpicum S, Pirotton M, Schleiss AJ (2008) Experimental and numerical analysis of flow instabilities in rectangular shallow basins. Environ Fluid Mech 8:31–54

    Article  Google Scholar 

  27. Choufi L, Kettab A, Schleiss AJ (2014) Bed roughness effect on flow field in rectangular shallow reservoir [Effet de la rugosité du fond d’un réservoir rectangulaire à faible profondeur sur le champ d’écoulement], Houille Blanche 83–92.

  28. Camnasio E, Orsi E, Schleiss AJ (2011) Experimental study of velocity fields in rectangular shallow reservoirs. J Hydraul Res 49:352–358

    Article  Google Scholar 

  29. Goltsman, A., and Saushin, I. (2019) Flow pattern of double-cavity flow at high Reynolds number, Physics of Fluids 31.

  30. Miozzi M, Romano GP (2020) Propagation of perturbations and meandering in a free surface shallow water jet. Experiments Fluids 61:065101

    Article  Google Scholar 

  31. Camnasio E, Erpicum S, Orsi E, Pirotton M, Schleiss AJ, Dewals B (2013) Coupling between flow and sediment deposition in rectangular shallow reservoirs. J Hydraul Res 51:535–547

    Article  Google Scholar 

  32. Dufresne M, Dewals BJ, Erpicum S, Archambeau P, Pirotton M (2010) Experimental investigation of flow pattern and sediment deposition in rectangular shallow reservoirs. Int J Sedim Res 25:258–270

    Article  Google Scholar 

  33. Yan H, Vosswinkel N, Ebbert S, Lipeme Kouyi G, Mohn R, Uhl M, Bertrand-Krajewski J-L (2020) Numerical investigation of particles’ transport, deposition and resuspension under unsteady conditions in constructed stormwater ponds. Environ Sci Europe 32:1–17

    Article  Google Scholar 

  34. Dominic JA, Aris AZ, Sulaiman WNA, Tahir WZWM (2016) Discriminant analysis for the prediction of sand mass distribution in an urban stormwater holding pond using simulated depth average flow velocity data. Environ Monit Assess 188:1–15

    Article  Google Scholar 

  35. Kantoush SA, De Cesare G, Boillat JL, Schleiss AJ (2008) Flow field investigation in a rectangular shallow reservoir using UVP LSPIV and numerical modelling. Flow Meas Instrum 19:139–144

    Article  CAS  Google Scholar 

  36. Peltier Y, Erpicum S, Archambeau P, Pirotton M, Dewals B (2015) Can meandering flows in shallow rectangular reservoirs be modeled with the 2D shallow water equations? J Hydraul Eng 141:04015008

    Article  Google Scholar 

  37. Dufresne M, Dewals BJ, Erpicum S, Archambeau P, Pirotton M (2011) Numerical investigation of flow patterns in rectangular shallow reservoirs. Eng Appl Comput Fluid Mech 5:247–258

    Google Scholar 

  38. Ferrara V, Erpicum S, Archambeau P, Pirotton M, Dewals B (2018) Flow field in shallow reservoir with varying inlet and outlet position. J Hydraul Res 56:689–696

    Article  Google Scholar 

  39. Kantoush SA, Bollaert E, Schleiss AJ (2008) Experimental and numerical modelling of sedimentation in a rectangular shallow basin. Int J Sedim Res 23:212–232

    Article  Google Scholar 

  40. Esmaeili T, Sumi T, Kantoush SA, Haun S, Rüther N (2016) Three-dimensional numerical modelling of flow field in shallow reservoirs. Proc Inst Civ Eng Water Manag 169:229–244

    Article  Google Scholar 

  41. Zahabi H, Torabi M, Alamatian E, Bahiraei M, Goodarzi M (2018) Effects of geometry and hydraulic characteristics of shallow reservoirs on sediment entrapment. Water (Switzerland) 10:1725

    CAS  Google Scholar 

  42. Lucas LV, Deleersnijder E (2021) Tracers and timescales: Tools for distilling and simplifying complex fluid mechanical problems. Water (Switzerland) 13:2796

    Google Scholar 

  43. Deleersnijder E, Delhez EJM (2007) Timescale- and tracer-based methods for understanding the results of complex marine models. Estuar Coast Shelf Sci 74:v–vii

    Article  Google Scholar 

  44. Deleersnijder E, Campin J-M, Delhez EJM (2001) The concept of age in marine modelling I. Theory and preliminary model results. J Mar Syst 28:229–267

    Article  Google Scholar 

  45. Bolin B, Rodhe H (1973) A note on the concepts of age distribution and transit time in natural reservoirs. Tellus 25:58–62

    Article  Google Scholar 

  46. Monsen NE, Cloern JE, Lucas LV, Monismith SG (2002) A comment on the use of flushing time, residence time, and age as transport time scales. Limnol Oceanogr 47:1545–1553

    Article  Google Scholar 

  47. Takeoka H (1984) Fundamental concepts of exchange and transport time scales in a coastal sea. Cont Shelf Res 3:311–326

    Article  Google Scholar 

  48. Xavier MLM, Janzen JG (2017) Effects of inlet momentum and orientation on the hydraulic performance of water storage tanks. Appl Water Sci 7:2545–2557

    Article  Google Scholar 

  49. Moncho-Esteve IJ, Palau-Salvador G, Brevis W, Vaas MO, López-Jiménez PA (2015) Numerical simulation of the hydrodynamics and turbulent mixing process in adrinking water storage tank. J Hydraul Res 53:207–217

    Article  Google Scholar 

  50. Sonnenwald F, Guymer I, Stovin V (2018) Computational fluid dynamics modelling of residence times in vegetated stormwater ponds. Proc Inst Civ Eng Water Manag 171:76–86

    Article  Google Scholar 

  51. Dewals B, Archambeau P, Bruwier M, Erpicum S, Pirotton M, Adam T, Delhez E, Deleersnijder E (2020) Age of water particles as a diagnosis of steady-state flows in shallow rectangular reservoirs. Water (Switzerland) 12:2819

    Google Scholar 

  52. Camnasio E, Erpicum S, Archambeau P, Pirotton M, Dewals B (2014) Prediction of mean and turbulent kinetic energy in rectangular shallow reservoirs. Eng Appl Comput Fluid Mech 8:586–597

    Google Scholar 

  53. Erpicum S, Meile T, Dewals BJ, Pirotton M, Schleiss AJ (2009) 2D numerical flow modeling in a macro-rough channel. Int J Numer Meth Fluids 61:1227–1246

    Article  Google Scholar 

  54. Stamou AI (2002) Verification and application of a mathematical model for the assessment of the effect of guiding walls on the hydraulic efficiency of chlorination tanks. J Hydroinf 4:245–254

    Article  Google Scholar 

  55. Mouchet A, Deleersnijder E, Primeau F (2012) The leaky funnel model revisited. Tellus Ser A Dyn Meteorol Oceanograph 64:19131

    Article  Google Scholar 

  56. Ahmed SS, Loewen MR, Zhang W, Ghobrial TR, Zhu DZ, Mahmood K, van Duin B (2022) Field observations of stratification in stormwater wet ponds. J Environ Manag 322:115988

    Article  CAS  Google Scholar 

  57. Song K, Xenopoulos MA, Buttle JM, Marsalek J, Wagner ND, Pick FR, Frost PC (2013) Thermal stratification patterns in urban ponds and their relationships with vertical nutrient gradients. J Environ Manag 127:317–323

    Article  CAS  Google Scholar 

  58. Pilotti M, Simoncelli S, Valerio G (2014) A simple approach to the evaluation of the actual water renewal time of natural stratified lakes. Water Resour Res 50:2830–2849

    Article  Google Scholar 

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Authors and Affiliations

  1. Research unit Urban & Environmental Engineering (UEE), Hydraulics in Environmental and Civil Engineering (HECE), University of Liege, Liege, Belgium

    Benjamin Dewals, Pierre Archambeau, Sébastien Erpicum & Michel Pirotton

  2. Institute of Mechanics, Materials and Civil Engineering (IMMC) & Earth and Life Institute (ELI), Université Catholique de Louvain, Louvain-La-Neuve, Belgium

    Eric Deleersnijder

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  1. Benjamin Dewals
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  2. Pierre Archambeau
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  5. Eric Deleersnijder
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Contributions

ED, BD and PA conceptualized the research and designed the methodology. BD and PA developed the computer codes for data analysis and performed formal analysis. BD wrote the original draft, which was revised by SE and ED MP provided expertise.

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Correspondence to Benjamin Dewals.

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Dewals, B., Archambeau, P., Erpicum, S. et al. What does the volume-averaged water age distribution function reveal about flow fields in rectangular shallow reservoirs?. Environ Fluid Mech 24, 75–93 (2024). https://doi.org/10.1007/s10652-024-09967-z

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